Question: Multiply the following complex numbers, marked as blue dots on the graph: $( e^{\pi i / 4}) \cdot (3 e^{\pi i})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{\pi i / 4}$ ) has angle $\frac{1}{4}\pi$ and radius $1$ The second number ( $3 e^{\pi i}$ ) has angle $\pi$ and radius $3$ The radius of the result will be $1 \cdot 3$ , which is $3$ The angle of the result is $\frac{1}{4}\pi + \pi = \frac{5}{4}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{5}{4}\pi$.